I should've used clearer terminology

It doesn't seem to me like the issue is one of terminology, but maybe I'm missing something.

Do you think giving examples [...] would help show that the really restrictive axiom is the archimedean one?

I'm not convinced that it is. The examples you give aren't ordered groups, after all.

It's unclear to me whether your main purpose here is to exhibit a surprising fact about ethics (which happens to be proved by means of Hölder's theorem) or to exhibit an interesting mathematical theorem (which happens to have a nice illustration involving ethics). From the original posting it looked like the former but what you've now written seems to suggest the latter.

My impression is that the blasé-ness is aimed more at the alleged application to ethics rather than denying that the theorem, quite mathematical theorem, is interesting and surprising.